Question 967·Easy·Math

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If $(x-3)^2 = 16$ , which of the following is a possible value of $x$ ?

A squared equation can have two solutions because a positive number and a negative number can have the same square. If the question asks for one possible value, you only need to find one branch. A Desmos regression with a restriction can do that; the trap is forgetting the negative branch.

Hints

Hint 1
A square root of $16$ is a number whose square is $16$ . Both $4$ and $-4$ work. What are the two possible values of the expression $x-3$ ?
Hint 2
The negative branch has $x-3<0$ , so $x<3$ . A Desmos regression can find a solution on that branch if you restrict it to $x_1<3$ .

Step-by-step

Keep both signs, then find one solution
Step 1
Recognize the two branches
Because $4^2=(-4)^2=16$ , the squared expression $x-3$ could equal $4$ or $-4$ : $x-3=4$ or $x-3=-4$ . Don't discard the negative case. Squaring hides whether the expression started positive or negative.
Step 2
Find a value on the negative branch
On the negative branch, $x-3<0$ , so $x<3$ . Type $(x_1-3)^2\sim16\{x_1<3\}$ in Desmos. Replacing $x$ with $x_1$ and $=$ with $\sim$ makes this a regression; the braces keep its search below $3$ . Under PARAMETERS, Desmos shows $x_1=-1$ . So $-1$ is a possible value of $x$ . Choice D.

Question 967·Easy·Math

Strategy

Hints

Step-by-step

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Strategy

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Step-by-step

Lessons that teach this